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Classification of General n-Qubit States under Stochastic Local Operations and Classical Communication in Terms of the Rank of Coefficient Matrix

Xiangrong Li Dept of math, UCI, USA Dafa Li Dept of mathematical sciences, Tsinghua University

Theoretical Physics mathscidoc:1702.39003

PHYSICAL REVIEW LETTERS, 108, 180502, 2012.5
We solve the entanglement classification under stochastic local operations and classical communication (SLOCC) for general n-qubit states. For two arbitrary pure n-qubit states connected via local operations, we establish an equation between the two coefficient matrices associated with the states. The rank of the coefficient matrix is preserved under SLOCC and gives rise to a simple way of partitioning all the pure states of n qubits into different families of entanglement classes, as exemplified here. When applied to the symmetric states, this approach reveals that all the Dicke states |l,n> with l=1,..., [n/2] are inequivalent under SLOCC.
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@inproceedings{xiangrong2012classification,
  title={Classification of General n-Qubit States under Stochastic Local Operations and Classical Communication in Terms of the Rank of Coefficient Matrix},
  author={Xiangrong Li, and Dafa Li},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170217233605668104466},
  booktitle={PHYSICAL REVIEW LETTERS},
  volume={108},
  pages={180502},
  year={2012},
}
Xiangrong Li, and Dafa Li. Classification of General n-Qubit States under Stochastic Local Operations and Classical Communication in Terms of the Rank of Coefficient Matrix. 2012. Vol. 108. In PHYSICAL REVIEW LETTERS. pp.180502. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170217233605668104466.
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